In general, an exhaust passage of an engine has a catalyst device for purifying an exhaust gas. The catalyst supported by the catalyst device fails to provide an excellent catalyst performance at a temperature lower than an activation temperature. Therefore, it is necessary to perform a warm-up operation for increasing a temperature of the catalyst to the activation temperature within a short time, at the time of engine start. JP2011-220210A discloses a warm-up operation for increasing the temperature of the catalyst in which the exhaust gas is heated by retarding an ignition timing. In addition, in the warm-up operation disclosed in the aforementioned document, in order to secure a good ignitability even by retarding the ignition timing, so-called stratified charge combustion is performed, in which spark ignition is generated while a fuel spray is concentrated in the vicinity of an ignition plug.
However, in the warm-up operation disclosed in the aforementioned document, if a heater is turned on even when a condition for performing the warm-up operation of the catalyst is established, homogeneous stoichiometric combustion is performed by retarding the ignition timing. Although such a warm-up operation is effective to secure a heating performance, it is not satisfactory for emission reduction. In particular, in the aforementioned document, there is no consideration for a liquid fuel amount adhered to a piston crown surface which is important to suppress the amount of particulate matters (PM) of the exhaust gas. Therefore, it is difficult to reduce a PM discharge amount (hereinafter, also referred to as a particulate number (PN)).
In view of the aforementioned problems, it is an object of the present invention to control the engine by activating the catalyst early and reducing the PN.